So much of origami is taught as straight-line, corner-to-corner, or edge-to-edge straight folding. How do you make smooth, curved folds along predetermined lines?
Apart from just carefully folding along the curve with your fingers, following techniques get used:
- Embossing the line with a pointed object or (better) a used-up ballpoint pen. Folding along such an embossed line results in a relatively smooth fold even if the curve is complex.
- For some models (mostly the organic-looking ones), wet folding can allow very smooth lines to be folded. This is sometimes combined with scoring the paper using your fingernails. Daniel Chang uses such a technique for folding his realistic human faces.
- Robert J. Lang famously uses a laser tool to score the crease pattern into the paper. I was able to fold from such paper in one of his workshops and the scored line looks a row of tiny perforations which weaken the paper and guide your hand when you fold along the line.
- Some folders (e.g. Ekaterina Lukasheva) use digital plotter-like tools for embossing the paper.
Machine-embossed lines (the latter two examples) are of course much more precise than those made by hand, but even a line manually scored using a ball point pen can be surprisingly precise.
They're really creases, not true "folds" so the secret I've found is to not try and form them on a flat surface the way you would a straight fold but, instead, fold them in mid-air using your fingers (and nails if you have them) to support and shape the creases.
- start a crease in the direction you want (mountain or valley) by bending the paper in the desired direction but do not attempt to fold it flush.
- use your thumb and forefinger above the paper to create a crease with the middle finger in the crease below it to keep the paper from collapsing completely.
- shape the curve as you move along the paper.
- go slow and be patient
If you want to make really detailed shapes, consider etching the creases in first with a tool.
I found it was easier to start in the center of the curve and work outwards in both directions to achieve the curved shape.
Here's a video showing the process... note that, in this case, the creases are pre-etched in since this is a purpose-made piece of paper but you should be able to use the same method without the pre-etching.